Results 1  10
of
12
Derivation of principal jump conditions for the immersed interface method in twofluid flow simulation
, 2009
"... Abstract. In a flow of two immiscible incompressible viscous fluids, jump discontinuities of flow quantities appear at the twofluid interface. The immersed interface method can accurately and efficiently simulate the flow without smearing the sharp interface by incorporating necessary jump conditi ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. In a flow of two immiscible incompressible viscous fluids, jump discontinuities of flow quantities appear at the twofluid interface. The immersed interface method can accurately and efficiently simulate the flow without smearing the sharp interface by incorporating necessary jump conditions into a numerical scheme. In this paper, we systematically derive the principal jump conditions for the velocity, the pressure, and their normal derivatives.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
"... On hypersingular surface integrals in the symmetric Galerkin boundary element method: application to heat conduction in exponentially graded materials ..."
Abstract
 Add to MetaCart
(Show Context)
On hypersingular surface integrals in the symmetric Galerkin boundary element method: application to heat conduction in exponentially graded materials
A class of Cartesian grid embedded boundary algorithms for incompressible flow with timevarying complex geometries
"... We present a class of numerical algorithms for simulating viscous fluid problems of incompressible flow interacting with moving rigid structures. The proposed Cartesian grid embedded boundary algorithms employ a slightly different idea from the traditional directforcing Immersed Boundary Methods; ..."
Abstract
 Add to MetaCart
(Show Context)
We present a class of numerical algorithms for simulating viscous fluid problems of incompressible flow interacting with moving rigid structures. The proposed Cartesian grid embedded boundary algorithms employ a slightly different idea from the traditional directforcing Immersed Boundary Methods; i.e. the proposed algorithms calculate and apply the forcedensity in the extended solid domain to uphold the solid velocity and hence the boundary condition at the rigidbody surface. The principle of the embedded boundary algorithm allows us to solve the fluid equations on a Cartesian grid with a set of external forces spread onto the grid points occupied by the rigid structure. The proposed algorithms use MAC (Marker And Cell) algorithm for solving the incompressible NavierStokes equations. Unlike projection methods, the MAC scheme incorporates the gradient of forcedensity in solving the pressure Poisson equation, so that the dipole force, due to the jump of pressure across the solidfluid interface, is directly balanced by the gradient of forcedensity. We validate the proposed algorithms via the classical benchmark problem of flow past cylinder. Our numerical experiments show that numerical solutions of the velocity field obtained by using the proposed algorithms are smooth across the solidfluid interface. Finally, we consider the problem of cylinder moving between two parallel plane walls. Numerical solutions of this problem obtained by using the proposed algorithms are compared with the classical asymptotic solutions. We show that the two solutions are in good agreement.
THE THREEDIMENSIONAL JUMP CONDITIONS FOR THE STOKES EQUATIONS WITH DISCONTINUOUS VISCOSITY, SINGULAR FORCES, AND AN INCOMPRESSIBLE INTERFACE ∗
"... Abstract. The threedimensional jump conditions for the pressure and velocity fields, up to the second normal derivative, across an incompressible/inextensible interface in the Stokes regime are derived herein. The fluid viscosity is only piecewise continuous in the domain while the embedded interfa ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. The threedimensional jump conditions for the pressure and velocity fields, up to the second normal derivative, across an incompressible/inextensible interface in the Stokes regime are derived herein. The fluid viscosity is only piecewise continuous in the domain while the embedded interface exerts singular forces on the surround fluids. This gives rise to discontinuous solutions in the pressure and velocity field. These jump conditions are required to develop accurate numerical methods, such as the Immersed Interface Method, for the solutions of the Stokes equations in such situations. Key words. Stokes equations, discontinuous viscosity, singular force, immersed interface method, jump conditions, incompressible interface, inextensible interface AMS subject classifications. 65N06, 65N12, 76Z05, 76D07, 35R05 1. Introduction. Biological
Contents lists available at ScienceDirect Applied Mathematics Letters
"... journal homepage: www.elsevier.com/locate/aml A numerical model for the transmembrane voltage of ..."
Abstract
 Add to MetaCart
(Show Context)
journal homepage: www.elsevier.com/locate/aml A numerical model for the transmembrane voltage of
a r t i c l e i n f o Article history:
, 2011
"... a b s t r a c t of years). The strength of mantle rocks varies with depth, with the elastic and viscous behaviors being different. The elastic moduli increase monotonically with depth, due primarily to the increasing pressure, with the shear modulus ranging approximately from 60 to 300 GPa and the b ..."
Abstract
 Add to MetaCart
(Show Context)
a b s t r a c t of years). The strength of mantle rocks varies with depth, with the elastic and viscous behaviors being different. The elastic moduli increase monotonically with depth, due primarily to the increasing pressure, with the shear modulus ranging approximately from 60 to 300 GPa and the bulk modulus ranging from about 100 to 600 GPa [1,9,15]. The viscous behavior is more complicated, with the viscosity decreasing with the depth above about 660 km. Below 660 km, there are conflicting 00219991/ $ see front matter 2011 Elsevier Inc. All rights reserved.
A numerical model for the transmembrane voltage of vesicles I
"... The Immersed Interface Method is employed to solve the timevarying electric field equations around a threedimensional vesicle. To achieve secondorder accuracy the implicit jump conditions for the electric potential, up to the second normal derivative, are derived. The transmembrane potential is ..."
Abstract
 Add to MetaCart
(Show Context)
The Immersed Interface Method is employed to solve the timevarying electric field equations around a threedimensional vesicle. To achieve secondorder accuracy the implicit jump conditions for the electric potential, up to the second normal derivative, are derived. The transmembrane potential is determined implicitly as part of the algorithm. The method is compared to an analytic solution based on spherical harmonics and verifies the secondorder accuracy of the underlying discretization even in the presence of solution discontinuities. A sample result for an elliptic interface is also presented.
UNIFORM ERROR ESTIMATES FOR NAVIERSTOKES FLOW WITH A MOVING BOUNDARY USING THE IMMERSED INTERFACE METHOD
"... Abstract. We prove that uniform accuracy of almost second order can be achieved with a nite difference method applied to NavierStokes
ow at low Reynolds number with a moving boundary, or interface, creating jumps in the velocity gradient and pressure. Difference operators are corrected to O(h) nea ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. We prove that uniform accuracy of almost second order can be achieved with a nite difference method applied to NavierStokes
ow at low Reynolds number with a moving boundary, or interface, creating jumps in the velocity gradient and pressure. Difference operators are corrected to O(h) near the interface using the immersed interface method, adding terms related to the jumps, on a regular grid with spacing h and periodic boundary conditions. The force at the interface is assumed known within an error tolerance; errors in the interface location are not taken into account. The error in velocity is shown to be uniformly O(h2j log hj2), even at grid points near the interface, and, up to a constant, the pressure has error O(h2j log hj3). The proof uses estimates for nite difference versions of Poisson and diffusion equations which exhibit a gain in regularity in maximum norm. Key words. NavierStokes equations,
uid interfaces,
uidstructure interaction, moving boundaries, immersed interface method, nite difference methods, Cartesian grid methods, maximum norm, error estimates, convergence, approximate projections AMS subject classications. 65N06, 65N12, 74F10, 76D05, 76D27, 35R05 1. Introduction. Recently